Chapter 14 Notes Part II

1. Chapter 14 Notes Part II Ideal Gas Law And Avogadro’s Principle

2. Gas Laws I Gay-Lussac’s Real vs. Ideal STP Boyle’s Charles’ P - T relationship Temp.: V - T relationship P - V relationship Gas laws are based on ideal gases - 273 K - 0°C direct - direct - inverse - Distinct volumes Pressure: multiply divide divide - 101.3 kPa - 760 mmHg - 760 torr Molecules are attracted to each other V1 V2 T1 T2 P1 P2 T1 T2 - 1 atm P1V1 = P2V2 T in Kelvin (°C + 273) T in Kelvin (°C + 273)

3. Gas Laws II Partial Pressures Combined Gas Law Ideal Gas Law T, P and D P1V1 P2V2 T1 T2 PV = nRT Density = m/v PTOT = P1 + P2 + P3 V must be in Liters NOTHING is constant! All units must be same V and D are: Inverse n = # of moles If any P PTOT will T must be in Kelvin! T and D are: Inverse R = constant depends on P If any P PTOT will P and D are: Direct T must be in Kelvin

4. Ideal Gas Law • When a gas behaves ideally (that is, it obeys the assumptions about gases in the kinetic theory) then it is possible to use the ideal gas law to define it.

5. Ideal Gas Law • Two factors make a gas not ideal; the fact that the particles will interact and that they do have volume. • Because of this, the relationship breaks down at very high pressures and very low temperatures.

6. Ideal vs. Real • In the real world, no gas is truly ideal • All gas particles have some volume, however small it may be • All gas particles also are subject to intermolecular forces • Gases will deviate from their “ideal” behavior at extremely high pressures and low temps.

7. Why? • As pressure increases and temperature increases, the amount of space between particles and the speed at which particles move decreases • If enough pressure is applied to certain gases, they will liquefy and therefore would not be a gas (examples: O2 and propane)

8. Ideal Gas Law PV=nRT P = pressure V = volume n = # of moles R = ideal gas constant T = temperature

9. Ideal Gas Law • The letter R is the ideal gas constant. • R’s value is 8.31 L kPa / mol K OR • R’s value is 0.082 L atm/mol K

10. Conversion factor 22.4 Liters = 1 mole

11. STP Remember STP is standard temperature and pressure where: temperature = 0oC or 273K pressure = 1atm or 101.3 kPa

12. PV=nRT R is a constant in units L kPa/ mol KORL atm/ mol K Where L= volume in liters kPa or atm= pressure in kilo pascals or atmospheres Mol= moles K= temperature in Kelvin

13. Practice Problem #1 • You fill a rigid container that has a volume of 20.0L with nitrogen gas to a pressure of 2150 kPa at 28oC. How many moles of gas are present?

14. Practice Problem #2 How many moles (n) of CO2 occupy a volume of 8 L at 18°C and a pressure of 90.7 kPa?

15. Practice Problem #2 cont. PV = nRT 90.7kPa (8L) = n(8.31)(291) 725.6 = n(2418.21) n = 725.6 2418.21 n = .3 moles

16. More Practice Problems! • What is the mass of the CO2 in the above example? • How many molecules of CO2 are in the above example?

17. How T and P effect Density • Recall that the equation for density = mass/volume. • Assuming that the # of particles in a sample of gas stays constant (thus keeping mass of the gas constant), the only variable that will change density is the volume of the gas.

18. How T and P effect Density • Note that an inverse relationship exists b/n density and volume. • Charles’s Law states that T and V are directly related. Thus, if T is increased, V will increase…causing density to decrease. *** T and density are inversely related ***

19. How T and P effect Density Boyle’s Law states that an inverse relationship exists b/n P and V. Thus, if P increases, V will decrease…causing density to increase. *** P and density are directly related ***

20. Density at STP • When calculating density at STP, assume that the mass of the gas remains constant unless you are told otherwise. • Use combined gas law to determine the V of the gas at STP (V2), and plug it into the density equation w/ the mass you were given.

21. Practice Problem Calculate the density of a gas at STP that was collected at 46C and 873 mmHg if 996 mL of the gas is present and has a mass of 5.22 g.

22. *** 1st…calculate V at STP *** 873(996) = 760(X) 319 273 X = 873(996)(273) 319(760) X = V2 = 979 mL Density = m/V = 5.22/979 Density = 5.33 x 10-3

23. More Gas Law Practice Problems • Calculate the volume that 0.881 mol of gas at STP will occupy

24. More Gas Law Practice Problems • At 0oC and 1atm pressure, a sample of gas occupies 30mL. If the temperature is increased to 30oC and the entire gas sample is transferred to a 20mL container, what will be the gas pressure inside the container?

25. More Gas Law Practice Problems • Determine the volume of a container that holds 2.4 mol of gas at STP. • What size container do you need to hold 0.0459 mol nitrogen at STP?

26. More Gas Law Practice Problems • Calculate the volume that 2.0kg of methane gas will occupy at STP

27. More Gas Law Practice Problems • Determine the Celsius temperature of 2.49 moles of gas contained in a 1.00 L vessel at a pressure of 143 kPa.

28. Apply Gas Laws to Gas Stoichiometry • What volume of oxygen gas is needed for the complete combustion of 4.00L of propane gas? Assume constant pressure and temperature

29. Practice Problems • What volume of oxygen is needed to react with solid sulfur to form 3.5L SO2

30. Practice Problems • Ammonium nitrate is a common ingredient in chemical fertilizers. Use the reaction shown to calculate the mass of solid ammonium nitrate that must be used to obtain 0.100L of dinitrogen gas at STP NH4NO3 (s)  N2O (g) + 2H2O

31. Practice Problems Solid potassium metal will react with Cl2 gas to form ionic potassium chloride. How many liters of Cl2 gas are needed to completely react with 0.204g of potassium at STP?